You probably remember the inspirational story from your childhood, The Little Engine that Could. Yes, I understand, that story is supposed to be inspirational…but I’ve always considered it pernicious. Pernicious. How can that be? Well, I was reminded of that… Read More ›
“You got an A in Algebra One in your previous school, but you clearly don’t know very much algebra. How did you get that A?” was my question to a certain high-school freshman I was teaching. No, it was not… Read More ›
In recent months I’ve been desultorily exploring ChatGPT, for better or for worse. In the following examples you might want to note GPT’s impressive use of English syntax and vocabulary, combined with an impressive amount of lying/inaccurate facts: Finally, as… Read More ›
Who am I talking about? Hypatia of Alexandria, of course. In March of 415 C.E. “she was murdered by a mob of Christians” (for some strange value of “Christians”) according to a well-sourced article in Wikipedia. To see why they… Read More ›
“Teachers deserve better. They deserve more trust and respect, and less standardized testing, smaller class sizes, and yes, larger paychecks.” So says author Alexandra Robbins in The Teachers: A Year Inside America’s Most Vulnerable, Important Profession. A well-known long-time New… Read More ›
Continuing to sing the praises of the under-appreciated Helen DeWitt, I must tell you about her language-learning proposal. For a bit of context, I will first tell you about a brief conversational exchange I had with my ninth-graders at Weston… Read More ›
Eight months ago I wrote a post about our first attempt at interdisciplinarity at the Crimson Summer Academy. It was a start. Perhaps even a good start, but still no more than a start. This summer we are keeping the… Read More ›
A friend of mine claims to have had a bad experience with trigonometry in high school. Is this because she had a bad teacher? (Most people blame their teacher.) Or is it because she was a bad student? Or is… Read More ›
They taught it once. They taught it twice. They taught it thrice. So, in the well-known (or perhaps no longer so well known) words of Charles Lutwidge Dodgson (definitely better known as Lewis Carroll), it must be true: “Just the… Read More ›
You’ve always wanted to learn the truth about the interaction between numbers and names, haven’t you? James Propp will be your teacher. In this month’s Mathematical Enrichments, he makes this observation: Poincaré once wrote “Mathematics is the art of giving… Read More ›
Over 97% of Americans are either immigrants or descendants of immigrants—even if some so-called conservatives don’t want to admit it. But many of us who grew up with immigrant parents or grandparents are unable to speak or read the language(s)… Read More ›
This puzzle comes from mathematical physicist John Baez. That’s John, not Joan (she is not a mathematical physicist, as far as I know), though they are in fact first cousins. You don’t normally expect that a physicist with a Ph.D…. Read More ›
“Nothing,” say some of my students. “You can always find the value of x,” say some others. “It’s useful in real life,” says one. “No it isn’t!” says another. By this point we’ve moved far afield from the original question…. Read More ›
Let’s suppose your unimaginative instructor gave you this task: add up all the whole numbers from 1 through 42. You have, of course, several options: Or, if your language of choice is APL, you could simply write a one-line program… Read More ›
We continue to hear concerns about Artificial Intelligence, especially ChatGPT, nearly every day. As the link in the previous paragraph will take you to my second post about ChatGPT, this must be the third, and I really don’t want to… Read More ›
The Next Generation. No, not Star Trek—we’re talking America’s Test Kitchen: The Next Generation on Amazon FreeVee. Normally I don’t like cooking competitions. But I continued to watch all ten episodes of this competition because of my love for the… Read More ›
You do remember Donald Rumsfeld, don’t you? Famous (or infamous) for many things, including the distinction between known unknowns and unknown unknowns, not to mention known knowns and unknown knowns. Confused yet? James Harbeck—whom I’ve cited a dozen times in… Read More ›
Americans don’t understand numbers—especially when those numbers are fractions. You may know the true story about Arby’s customers who were convinced that a new ⅓-pound burgers contained less meat than the familiar ¼-pounder, since 4 is larger than 3. Maybe… Read More ›
“Why do you want to mix our children with city blacks? We moved here to get away from that element.” So said a resident of Lincoln, Massachusetts. A white resident, needless to say. Shocking perhaps, but not surprising, even if… Read More ›
Learning Strategies 